Well, you have the natural born Texans (the folks who've been here for generations), the transplanted Texans (folks who were born elsewhere, but moved here for one reason or another, and assimilated the accent), and those who are the children of the transplants. I'm in the last category, my folks are in the second. They're originally from Chicago, but they've been here for the last 40 years; they don't say "y'all" or anything like that, but they also don't sound like they're from Chicago. I say "y'all" and everything else, but my voice also has a slight Chicago tinge to it, especially whenever I say "sahcks" or "lahbster."
However, no one in our family orders a "pop" anymore!